Democrats contend that is nonsense. They say Ryan’s plan would cut taxes disproportionately for the wealthy, eliminate most or even all “discretionary” programs that aren’t defense-related, end today’s version of Medicare, drop many tax deductions that help average Americans, and worsen the economy.

This may sound like the usual partisan squabble, especially since Mitt Romney has risked turning the presidential campaign into a referendum on Ryan’s plan by making the Wisconsin congressman his running mate. Yet what’s indisputable is this: The Ryan plan will work only if his theoretical assumptions hold up — and that’s hard to gauge with so few details and so many variables.

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Under the Ryan plan, for example, taxpayers in the lowest fifth of income would see their taxes increase slightly. Those earning $40,000 to $70,000 would get a $739 cut, and those in the top 0.1 percent would get a $773,000 cut. But financing for those cuts remains vague; the Ryan plan said they will be paid for by eliminating various unnamed tax deductions.

Ryan’s plan “aggressively cuts tax rates and promises to recoup lost revenue by getting rid of tax preferences; but what it fails to do is specify which tax preferences it will get rid of, kicking that over to others in Congress to do the heavy lifting,” said Roberton Williams, a senior analyst at the nonpartisan Tax Policy Center.

The most immediate impact of Ryan’s plan would be twofold: a doubling-down on the Republican supply-side theory that cutting taxes, especially for the wealthy, will spur growth and increase revenue; plus a potentially unprecedented shrinking of government spending. In Ryan’s view, these measures, along with a revamp of Medicare and other actions, would be the elixir the economy needs
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An analysis of Ryan’s plan by the nonpartisan Congressional Budget Office, released in March, made clear that Ryan’s economic assumptions are key to his plan. For example, the report said that under one current scenario the federal debt would be 200 percent of the nation’s gross domestic product in 2050. But under the scenario envisioned by Ryan, the public debt would be just 10 percent of GDP by 2050.

The depth of the nation’s fiscal problems is so great that, even with Ryan’s assumptions, his plan would not balance the budget until 2040, but that is sooner than under existing laws, according to the budget office.

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Ryan’s assumptions provide the key to understanding his political thinking. He predicts that his plan would bring in more revenue from increased economic activity even while cutting the top tax rate and corporate rate from 35 percent to 25 percent, adopting the supply-side theories that he has subscribed to since he was at Miami University of Ohio.

Ryan also believes that, even while cutting tax rates, revenues would go from 15.5 percent of GDP to 19 percent in 2030.

The effectiveness of cutting tax rates in anticipation of boosting economic activity has been the subject of debate for years and has escalated since the Bush-era tax cuts have been followed by large deficits.

By failing to say which tax deductions would be eliminated, Ryan’s plan has left analysts to wonder whether that would lead to the end of the deduction for mortgage interest, charitable contributions, or other big-ticket items. Nor does the Ryan plan provide details about many spending cuts. The plan was passed by the House earlier this year but rejected by the Senate. Romney has said that the plan is “marvelous” but more recently said he was running on his own plan, which also is short on many specifics.

Patrick Louis Knudsen, a senior fellow at the conservative Heritage Foundation who until last year was a staffer of the House Budget Committee chaired by Ryan, said the plan should be viewed as a vision, not a final blueprint.

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“He made it very clear from the start that his aim was to use the committee as a forum to change the direction of government and, in particular, to reform entitlement programs,” Knudsen said.

On the surface, the cuts to entitlement programs could seem alarming, said Knudsen, who accused critics of attempting to scare seniors and the poor. “It’s easy to scare people and make it sound like a lot of money. But if the aim is to get people off food stamps, then it makes sense to cut spending. . . . It’s not as if we’re slashing government in half. You’d still have a fairly large federal government.”

Richard Kogan, a budget analyst with the Center on Budget and Policy Priorities, said the plan leaves the details of the cuts to members of the House Appropriations Committee.

“If he doesn’t say which programs he’s cutting, that allows for wishful thinking, assuming they won’t be cut or people assuming the worst. It doesn’t facilitate rational debate about a policy if there is no policy,” Kogan said.

Some details, however, have been released. The Ryan budget would slash food stamps by $134 billion over 10 years, affecting 47 million recipients, including 857,000 in Massachusetts. A typical family of four could lose about $90 a month in food stamps , according to the budget policy center.

At the same time, Ryan vows to protect defense spending. Indeed, if his plan is coupled with Romney’s vow to increase Pentagon dollars, there would be little or no room for nondefense spending outside of programs such as Social Security, budget analysts said.

One of the best-known and most controversial parts of Ryan’s budget is his plan to partially privatize Medicare by introducing a voucher program and to raise the program’s eligibility age from 65 to 67 by 2034.

On Monday, the Obama campaign blasted Ryan’s plan in a Web ad featuring people from Florida, a state full of Medicare enrollees where Romney was campaigning.

Republicans have defended against such attacks by noting that no one currently younger than 55 would be affected by the changes to Medicare and that even in 2023, when the voucher program would begin, seniors would retain the option to enroll in the existing, fee-for-service system — a choice they would not have been offered under earlier versions of Ryan’s plan.

Seniors who elected to go with vouchers — officially called premium support payments — would use them to purchase health insurance in a private Medicare marketplace.

The risk is that if private competition in the Medicare marketplace did not hold down insurance costs, government vouchers — whose annual increases would be capped — could cease to cover plan premiums over time. In this case, more people would chose the traditional fee-for-service model and cost savings for the government would not materialize.

Ryan’s plan does not include an estimate for Medicare savings after 2023, when the private marketplace would be introduced. It aims to save $205 billion between 2013 and 2022, on top of the $700 billion in Medicare spending reductions contained in Obama’s national health care law.

Though his plan calls for repeal of the health care law, Ryan would keep and expand Obama’s Medicare cuts, a departure from Romney’s plan to wipe out the law and his sharp criticism of the Medicare cuts.

Although the Ryan budget takes a gradual approach to a Medicare overhaul, it proposes swifter changes to Medicaid — $810 billion in federal spending reductions over the next 10 years.

As with Medicare, Ryan’s chief objection to Medicaid is its open-ended payment system. Ryan would scrap fee-for-service Medicaid in favor of Medicaid block grants to states, which would be adjusted annually, according to inflation and population growth.

He argues state governments are capable of reducing Medicaid costs and improving coverage options for recipients but have failed to do so for two reasons: They lack incentive, because the US government foots most of the bill, and flexibility, because they do not fully control eligibility requirements.